The long-term objective of this project is to develop new methods for marrow transplantation using alternative donors for patients with hematologic malignancies who lack an HLA identical sibling. Specific aims are: 1) to decrease morbidity and non-relapse mortality in transplants from unrelated donors. Human recombinant GM-CSF administered from day 0 to day +27 will be evaluated in a placebo-controlled, randomized, double-blind, phase III trial for the effect on engraftment, infection and regimen related toxicity. 2) to compare the outcome of transplants from unrelated donors who are partially HLA mismatched to those who are phenotypically HLA matched. Donors who differ by one HLA class I locus if the mismatched antigens fall within a crossreactive group, or differ by an HLA-DRB1 locus if the mismatched alleles fall within a single serologically defined specificity will be used for patients below 36 years of age. The rates of acute GVHD, transplant-related mortality and survival will be compared for patients with same age, disease, diagnosis and stage, and GVHD prophylaxis but different degree of HLA matching and 3) to decrease graft rejection and GVHD in recipients of HLA haplomismatched family member grafts. T-cell receptor/CD3 complex-specific antibody BC3 administered for 14 days beginning just before the marrow infusion will be evaluated in a phase I/II study to facilitate engraftment in patients with a positive anti-donor lymphocyte crossmatch, a group with the highest risk of graft rejection. 4) develop and assess functional assays that measure donor immune responses to the recipient's alloantigens, and determine if these assays will be useful for predicting GVHD and facilitating donor selection.